Mon Prof Augmenté
Five Doubling Columns
Age 16 · Maths
A row of five red columns grows taller from left to right, each one twice the height of the previous column. If the first height is u_0 and the fixed ratio is q, the height after n steps is u_n = u_0 × q^n.
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Age 16: open this week
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In the picture
- Shortest column: starting height u_0
- Second column: height after one multiplication by q
- Third column: height after two multiplications by q
- Fourth column: height after three multiplications by q
- Tallest column: height after four multiplications by q
Examples
- A ball bouncing to half its previous height each time
- A population growing by the same factor each year
Key takeaways
- Each term is the previous term multiplied by a fixed ratio q.
- The general term is u_n = u_0 × q^n.
Quiz: Five Doubling Columns (Age 16)
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In a geometric sequence, how do you get each term from the previous term?
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If u_0 is the starting height and q is the fixed ratio, which formula gives the height u_n after n steps?
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Starting from u_0, what is the height after two multiplications by q?
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